I am a beginner in this quantum-mechanics stuff. I understand the quantum eraser only from an experimental view. So I didn't understand the formalism that describes the quantum eraser. But what does the experiment tells us? Does the photon know that there is somebody watching it? And this is why it behaves in another way? Does the photon also see the future?

Obligatory: see "No Math, please". Any answer that is accurate without math is likely to be confusing; any answer that is simple without math is likely to be wrong. The formalism is required to answer this right.
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spencer nelsonFeb 28 '11 at 6:07

3 Answers
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No, the photon doesn't see anyone watching it. And the photon doesn't see its future, either. In fact, the photon doesn't exist in any classical sense prior to its observation.

All of its properties - e.g. which slits it could be taking; whether it behaves more as a particle or a wave etc. - are encoded in the wave function until the very moment of the measurement which is why they may always be "changed back" to the previous answers. For example, in quantum eraser, the photon is ordered to behave as a wave again, even though a premature argument could lead a sloppy person to think that the photon has already decided to behave as a particle forever.

When you measure the photon, it is finally possible to think of its properties classically and the wave function allows one to calculate all probabilities that the outcome will be something or something else. In the case of the quantum eraser, we restore the interference pattern. But any attempt to "imagine" that the photon has obtained a classical property at any moment before it was measured would lead to wrong predictions.

It is always essential to appreciate that the photon always behaves according to the laws of quantum mechanics and we're never allowed to approximate it by any classical intuition because the classical intuition fails. This strict requirement that classical mechanics is wrong may only be partly circumvented after the photon is actually detected (because then it interacts with a classical object that quickly decoheres) - but not earlier than that. In other words, quantum mechanics always holds: that's the main lesson of this experiment (and many others).

Sb1 says that it was remarkable that the experiment behaved as Scully and Druhl predicted. I disagree with this wording. The prediction could have been made by any father of quantum mechanics - no new physics was used whatsoever and they could predict the behavior of any setup of this kind. It could have been remarkable in the 1920s but after the 1920s, all such experiments were mundane physics.

I don't agree. that an experiment confirms existing theory can also be remarkable, if the theory predicts something highly counter-intuitive. This gives strong emotional confidence on QM, and that is always remarkable, just like the EPR experiment was.
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lurscherFeb 28 '11 at 15:32

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Perhaps I'm missing something, but can you edit this answer to include, specifically, what about the quantum eraser experiment is quantum? I can show, classically, that two orthogonal polarization states (of classical light) will not interfere, while changing to non-orthogonal polarization states will. Basically I have a problem with the tagging method which was used by Walborn et al. To me, it appears they are measuring the classical electromagnetic wave properties, and NOT probabilities and probability wave entanglement.
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daaxixJan 4 '13 at 22:55

@daaxix Same here. So far in all such experiments I've come across polarizers were used, and to me that is pretty controversial.
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jwalkerJan 27 '14 at 19:41

@daaxix, the classical electromagnetic description may be OK for any kind of interference-like experiment including complex ones but the interference may be shown to persist even if the photons are being sent one-by-one so that they create individual dots, so the interference is a property of a single photon as well, and that requires quantum mechanics.
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Luboš MotlJan 27 '14 at 20:10

@LubošMotl, not really. I'm not saying that light is not quantized, but suppose for a moment that light packets were detected with solid state sensors (which are quantum mechanical), then those interference patterns would still be "individual dots" caused by the sensor, NOT necessarily the photons, with the polarizers still causing the interference. Has anyone disentangled this problem?
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daaxixJan 28 '14 at 5:54

"Quantum eraser" was first proposed by M. Scully and K. Druhl. In order to understand it, we must know the famous double slit experiment first which I suppose you already know. You must be aware that in the double slit experiment if photons are emitted one at a time an interference pattern forms at the detector screen. As soon as you try to observe which path the photon follows that is which slit it passes through, left or right slit, the interference disappears. That means a knowledge of "which path" information destroys the wave like character of a photon and hence no interference possible. But in 1982, Scully and Druhl suggested a stunning modification of the experiment. They proposed the following on the basis of their quantum mechanical calculation.

Suppose a tagging device is attached by which we can know the "which path" information of the photon. Now if, just before the photon hits the detector screen, we eliminate the possibility of our knowledge of the "which path" information by erasing the mark registered by the tagging device, both possibilities that is the photon passed through the left slit and photon passed through the right slit should come back into play. Both histories should come back once again and interference pattern should reemarge. As if we are kind of shaping the past (warning: it is by no means that future is affecting the past).

Experiment carried out by Raymond Chiao, Paul Kwiat and A. Steinberg. Remarkably it worked just as scully and Druhl predicted. Interference pattern indeed reemarged.

great explanation! can you elaborate a bit on the tagging mechanism used to know 'which path' the photon took?
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lurscherFeb 28 '11 at 15:27

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@lurscher: Thanks. Briefly, it is a device which permits a photon to freely pass through a slit but forces its spin axis to point to a definite direction. Devices in front of the two slits make the photons spin in a different but specific manners. The detector screen registers a dot at the photon's impact position as well as keeps record of the photon's spin direction.
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user1355Feb 28 '11 at 15:45

how does the "erasing the mark" procedure is made?
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HDEMar 1 '11 at 11:39

All the other explanations are wrong. The light does not interact with itself anymore because the light is polarized. Only waves polarized in the same direction can interfere with each other. It's just another dimension. Do a "measurement" that doesn't use interference and it won't work.

A photon has no memory, but the photon/electromagnetic wave "knows" its polarization and only reacts (interferes) with waves polarized the same way.

There is no waveform that collapses by observation, the only thing that happens is that the measurement is not actually a measurement but a change of the system. A pure measurement would only measure and not disturb the process.